Mathematical instrument.



A. GARINGER.

MATHEMATICAL INSTRUMENT.

APPLICATION FILED AP ILI. 1911.

Patented Dec. 5, 1911.

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ALBERT GARING-ER, 0F STAMFORD, CONNECTICUT.

MATHEMATICAL INSTRUMENT.

Specification of Letters Patent.

Application filed April 1, 1911.

Patented Dec. 5, 1911.

Serial No. 618,381.

To all whom it may concern:

Be it known that I, ALBERT GARINGER, a citizen of the United States, and a resident of the city of Stamford, in the State of Connecticut, have invented certain new and useful Improvements in Mathematical Instruments, of which the following is a specification. 7

My invention relates to devices for drawing curves, and particularly curves of the type known as conchoid curves, and also adapted to be used in the solution of the problem of the trisection of an angle.

In the accompanying drawings, Figure 1 is a plan view of an embodiment of my invention adapted to draw or trace a conchoid curve, and to trisect an angle; Fig. 2 is a vertical section across the junction of the arms 26 and 28; Fig. 3 is a diagram demonstrating the solution of the problem of the trisection of an angle; Fig. 4 is a plan view.

of a modification of my invention; Fig. 5 is a side elevation of thesame, partly insection, looking toward the member 12; and Fig. 6 is a vertical section along the line 6-6 of Fig. 4.

In carrying my invention into effect, in the form shown. on Sheet 1 of the accompanying drawings and more completely in Fig. 1, I provide a right-angled member having the two arms 22and 26, which member is pivotally attached by the pivot 30 to the arm 29, which in its turn is secured to The arm 22 the arm 28 by the pivot 32. carries an extension slide 23, and the arm 26 is provided with a slot 27. The arms 26 and 28 must always be perpendicular to each other, and they are secured together by the set-screw 11, which is adapted to be screwed down into the rectangular upwardly projecting stud 10 of the block 37, which stud slides in the grooves 27 of the arm 26. The block 37 slides over the arm 28, and when the screw 41 is tightened it holds the arm 26 in place against longitudinal movement. The member 21 is secured to the right-angled member by a pivot 35 which passes through the slot 27 in the arm 26, and said member 21 has a slot 31 in its enlarged end portion in which slides an extension of the pivotal joint 32. The other end of the member 21 is provided with an opening 25 to receive a tracing point. It should be noted that the distance between the center of the pivot 35 and the opening 25 must be exactly twice the distance from the center of the pivot 30 to the center of the pivot 32.

The operation of this form of my invention in tracing a conchoid curve is as follows: The center of the pivotal joint 32 rep resents the focus of the conchoid curve to be drawn, and is placed upon such focus. The center line of the arm 26 represents the directrix of such curve, and is placed thereupon and held stationary. A pencil or tracing point is then placed in the opening 25of the member 21 whereupon the conchoid curve 33 may be traced. The operation of this form of invention in trisecting an angle may be described as follows, having reference to the formshown in Fig. 1. The opening 24 in the extension arm 23 is brought into register with the opening 25 in the arm 21. The center of the pivot 32 is then placed on the vertex of the angleto be trisected, the inner edge of the arm 29 laid along one side of the angle and the inner edge of the arm 28 laid along the other side of the angle. It will be seen that when the said members are placed in the above positions, a line joining the central points of the pivots 32 and 35 and which when extended lies along the edge 34 of the member 21, will measure off one-third of the angle included between the members 28 and 29. The proof of this proposition may be demonstrated by a consideration of Fig. 3. In that view the line X-X is analogous to the middle line of the member 26, A C to the inner edge of the member 29, A B to the inner edge of the member 28, A D E F to the edge 34 of the member 21, and C H F to the middle lines of the member 22 and extension member 23. Now let the angle C A B in Fig. 3 be any angle, and let the line X-X. be drawn perpendicular to A B through C, then XX' will be the directrix and A the focus. Then draw C F perpendicular to X-X', draw D F through A equal to twice A C, let E be the middle point of D F, then F E equals E D equals A C. Draw E H parallel to X-X at the middle point of C F; then F E equals E D as F H equals H C; then E C equals E F equals E D equals C A; then the angle D E O equals twice the angle E F H; then the angle D A C equals twice the angle D A B, and the angle 0 A B has one-third divided off, and upon the bisection of thi angle D A C the angle 0 A B is trisecte In carrying my invention into efiect in the form shown in Fig. 4, I provide three members of suitable size, designated 10, 11 and 12. The member 10 is provided with a slot 13, andthe member 12 is provided with a slot 14. The member 11 need have no slot. The members are united together or assembled as shown in the drawings, the members 10 and 11 being pivotally connected by means of a screw pivot 20 and wing-nut 15, which allow them to swing freely one upon the other when loose but which may be tightened so as to hold them firmly at any determined angle with regard to each other. The members 11 and 12 are united by means of a pivot which passes through a perforation in the end of the member 11 and slides freely in the slot 14: in the member 12, so that the member 12 may always swing freely in angular relation to the member 11, and also have a certain amount of movement longitudinally with respect to the member 11. The member 12 is also provided with a pivot 17 which slides freely in the slot 13 of the member 10, thus permitting a certain amount of swing or lateral movement to the member 12 with relation to the member 10. It will be noticed that if the wing-nut 15 be tightened so as to hold the members 10 and 11 in rigid relation to each other, the member 12, if it move at all, must move in a certain relation to both of the members 10 and 11. The member 12 is provided at its outer or free end with means, as the perforation 18, adapted to receive a pencil or other tracing or drawing point. The operation of this form of my invention is as follows: The member 11 having been firmly fixed in any desired relation to the member 10 by means of the wing-nut 15, the member 12 is swung around on the pivot 16, whereupon the free end will trace a conehoid curve, of which the pivot 16 occupies the position of the focus, and the member 10 represents the directrix.

Having thus described my invention, what I claim as new, and desire to secure by Letters Patent, is as follows:

1. An instrument for tracing conohoid curves, comprising a stationary member,

corresponding to the direct-rix of the curve and provided with a slot, a member pivotally connected to said first named member and adapted to be firmly set at a determined angle with regard to said first named member, and a swinging member adapted to bear a tracing point and provided with a slot and pivotally connected in said slot to said second member at a point corresponding to the focus of the curve, and provided with a fixed pivot sliding in the slot of the first named member.

2. An instrument for tracing conohoid curves and trisecting angles, comprising a right-angled member having an arm 22 provided with an extension arm 23 and an arm 26 provided with a slot 27; a member 21 provided with a slot 31 and a stud or pivot 35 engaging in said slot 27; and members 29 and 28 pivotally secured together and slidingly secured in said slot 81, the outer end of the member 29 being pivotally secured to the angle of said arms 22 and 26 and the member 28 bearing a set screw engaging with the block engaging in said slot 27, whereby the member 28 may be secured at any point in said slot 27 but be held always perpendicular to said member 26.

In witness whereof, I have hereunto set my hand in the presence of two witnesses.

ALBERT GARINGER.

Witnesses:

HARRY QOHAN, LILIAN M. WARNER.

Copies of this patent may be obtained for five cents each, by addressing the Commissioner of Patents,

Washington, I). G. 

